The Blog of Scott AaronsonIf you take just one piece of information from this blog:Quantum computers would not solve hard search problemsinstantaneously by simply trying all the possible solutions at once.

Update: I submitted the following response to the comments over on Lubos’s blog. Since it has some bits of general interest, I thought I’d crosspost it here while it awaits Lubos’s moderation.

Since Lubos “officially invited” me to respond to the comments here, let me now do so.

1. On “loopholes” in quantum mechanics: I completely agree with Lubos’s observation that the actual contents of my book are “conservative” about the truth of QM. Indeed, I predict that, when Lubos reads his free copy, he’ll agree with (or at least, have no objections to) the vast majority of what’s in the book. On the other hand, because I was guest-blogging about “the story of me and Lubos,” I found it interesting to highlight one area of disagreement regarding QM, rather than the larger areas of agreement.

2. On Gene Day’s patronizing accusation that I don’t “get the basics of QM or even comprehend the role of mathematics in physics”: his misreading of what I wrote is so off-base that I don’t know whether a response is even necessary. Briefly, though: of course two formulations of QM are mathematically equivalent if they’re mathematically equivalent! I wasn’t asking why we don’t use different mathematical structures (quaternions, the 3-norm, etc.) to describe the same physical world. I was asking why the physical world itself shouldn’t have been different, in such a way that those other mathematical structures would have described it. In other words: if you were God, and you tried to invent a theory that was like QM but based on those other structures, would the result necessarily be less “nice” than QM? Would you have to give up various desirable properties of QM? Yes? Can you prove it? The ball’s in your court, Mr. Day — or else you can just read my book! 🙂

3. On Lord Nelson’s accusation that I’m a “poseur”: on reflection, someone who only knew me from blog stunts like this one could easily be forgiven for getting that impression! 🙂 So it might be worth pointing out for the record that I also have a “day job” outside the blogosphere, whose results you can see here if you care.

4. On my political views: I wish to clarify for Tom Vonk that I despise not only “Communists,” but the ideology of Communism itself. One of the formative experiences of my life occurred when I was an 8-year-old at Wingate Kirkland summer camp, and all the campers had to relinquish whatever candy they’d brought into a communal “bunk trunk.” The theory was that all the campers, rich and poor alike, would then share the candy equally during occasional “bunk parties.” What actually happened was that the counselors stole the candy. So, during a meeting of the entire camp, I got up and gave a speech denouncing the bunk trunk as Communism. The next day, the camp director (who had apparently been a fellow-traveler in the 1950s) sat with me at lunchtime, and told me about a very evil man named Joe McCarthy who I was in danger of becoming like. But the truth was that I’d never even heard of McCarthy at that point — I just wanted to eat candy. And I’d give exactly the same speech today.

Like (I suppose) several billion of the world’s people, I believe in a dynamic market-based capitalist society, and also in strong environmental and other regulations to safeguard that society’s continued existence. And I don’t merely believe in that as a cynical compromise, since I can’t get the “dictatorship of the proletariat” that I want in my heart of hearts. Were I emperor of the world, progressive capitalism is precisely what I would institute. In return, perhaps, for paying a “candy tax” to keep the bunk functioning smoothly, campers could keep their remaining candy and eat or trade it to their heart’s delight.

5. On climate change: I’m not a professional climatologist, but neither is Lubos, and nor (correct me if I’m wrong) is anyone else commenting here. Accordingly, I refuse to get drawn into a debate about ice cores and tree rings and hockey sticks, since my experience is that such debates tend to be profoundly unilluminating when not conducted by experts. My position is an incredibly simple one: just like with the link between smoking and cancer, or the lack of a link between vaccines and autism, or any other issue where I lack the expertise to evaluate the evidence myself, I’ll go with what certainly looks like an overwhelming consensus among the scientists who’ve studied the matter carefully. Period. If the climate skeptics want to win me over, then the way for them to do so is straightforward: they should ignore me, and try instead to win over the academic climatology community, majorities of chemists and physicists, Nobel laureates, the IPCC, National Academies of Science, etc. with superior research and arguments.

To this, the skeptics might respond: but of course we can’t win over the mainstream scientific community, since they’re all in the grip of an evil left-wing conspiracy or delusion! Now, that response is precisely where “the buck stops” for me, and further discussion becomes useless. If I’m asked which of the following two groups is more likely to be in the grip of a delusion — (a) Senate Republicans, Freeman Dyson, and a certain excitable string-theory blogger, or (b) virtually every single expert in the relevant fields, and virtually every other chemist and physicist who I’ve ever respected or heard of — well then, it comes down to a judgment call, but I’m 100% comfortable with my judgment.

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Ronald: Awesome! I actually noticed that the original was in the Rijksmuseum (it says so on the back cover of my book), and thought about seeing it on my next visit to Amsterdam. Look forward to doing so!

Pangloss #6: No plans for a book tour, though maybe CUP would finance one if enough people starting buying the book! 🙂 But do stop by my office if you’re ever in the Boston area, and I’ll happily sign your copy.

“Let’s be clear: the work of science has nothing whatever to do with consensus. Consensus is the business of politics. Science, on the contrary, requires only one investigator who happens to be right, which means that he or she has results that are verifiable by reference to the real world. In science, consensus is irrelevant. What is relevant is reproducible results. The greatest scientists in history are great precisely because they broke with the consensus.”

-Michael Crichton

There is a consensus over the warming trend. Otherwise there is hardly a consensus, Scott, only proclamations and statements that there is no debate. The discussion has become political. There is plenty of skepticism over modelling, what actions to take, if any, and whether or not geo-engineering would be harmful.
Bertrand Russell said his grandmother gave him his only advice from the Bible that was useful: “Do not follow the multitude to do evil.” Substitute “consensus”.

Gordon #8: That Michael Crichton quote is one of the dumbest things I’ve ever read.

(Indeed, notice how you yourself hypocritically follow it with “There is a consensus over the warming trend. Otherwise there is hardly a consensus,” thereby implicitly acknowledging the importance of consensus, and contradicting the quote!)

What actual policymaking implications would Crichton’s quote have, were it taken seriously? Would you agree with those implications in any other field? For example: should politicians decide that, if even one scientist believes that HIV doesn’t cause AIDS, that scientist should be listened to over the “consensus” of every other scientist, if they (the politicians) decide that the renegade “happens to be right”? As you might know, the former President of South Africa, Thabo Mbeki, made exactly that decision, thereby causing hundreds of thousands of preventable deaths (at least according to “consensus” estimates). Was he justified?

If nothing else, the last line of Crichton’s quote should be amended to read: “The greatest scientists in history are great precisely because they changed the consensus.” (Or as Carl Sagan once put it: “Yes, they laughed at Galileo, they laughed at Einstein. But they also laughed at Bozo the Clown.”)

Ultimately, Crichton’s quote trades on a trivial confusion between the scientific process and the results of that process (insofar as the results are knowable at any one time). As soon as that distinction is pointed out, Crichton’s “reasoning” collapses.

Yes, the only way science ever progresses is by someone challenging the consensus, and winning. But precisely because the scientific consensus is open to challenge in that way, the results of the scientific process at any given time are generally the most reliable guide to truth that’s available at that time.

(A delicious irony: I’d think that, of all people, those who call themselves “free-market capitalists” would understand the above logic! For it’s nothing more than the scientific analogue of the “central insight of capitalism”: that at any given time, the price a commodity is trading at is the best publicly-available estimate of the commodity’s value.)

My conclusion is that, if you’re a climate skeptic, then your aspiration should indeed be to go up against the scientific consensus and change the consensus—that’s the one speck of truth in Crichton’s quote! Because if you can’t change the consensus, then why should people in the wider world believe you, and not believe the consensus?

“(Indeed, notice how you yourself hypocritically follow it with “There is a consensus over the warming trend. Otherwise there is hardly a consensus,” thereby implicitly acknowledging the importance of consensus, and contradicting the quote!)”

Gordon is doing nothing of the kind; he is pointing out that your assertion of fact concerning an alleged consensus, on which you base your argument, is false.

Your basic error is your refusal to make any attempt to judge the scientific arguments for yourself. Anyone is capable of judging whether the arguments offered make sense; no one has to take scientists’ word for it, even people with much less education than you. And no one should, given what is at stake. What counts is not what politicians think, but what the voters think, and think is what they should do, including you!

biff33: I could tell you that I went through a phase years ago when I read dozens of books and articles about climate change (both sides), and that I found the mainstream scientific case vastly more persuasive than the skeptics’ case.

To tell you the truth, I wasn’t very impressed by the climatologists’ sophisticated computer models—I actually agree with the skeptics that we don’t yet know for sure whether those models are more reliable than crude back-of-the-envelope calculations. What impressed me more was that in any case, the crude back-of-the-envelope calculations predict basically the same thing as the sophisticated computer models anyway! Namely, they predict that current human GHG emissions should be more than enough to produce warming that would have profound effects on human life. And as Nate Silver (not known for making bad predictions) discusses in his recent book, the magnitude of the observed warming over the last century is strongly consistent with what the crude back-of-the-envelope calculations suggested all along.

What I found particularly revealing was that, if you go back to before climate change became a political issue, then you find scientists like Svante Arrhenius (in the late 19th century) or John von Neumann (in the 1950s) discussing how human CO2 emissions would noticeably raise the earth’s temperature as an obvious consequence of established physics and chemistry—that’s what it looked like to them!

Anyway, I could tell you all this, but I’ll presume that you read all the same sorts of things that I read and came to different conclusions. So then the question becomes: how can we decide which one of us is right? We could try hashing out the details on this blog—but suppose (as experience suggests is likely) we debate about ice cores and tree rings for months, and we still don’t come to an agreement? Should we spend our whole lives arguing about it? If we don’t have time for that, then the only alternative I see is to defer to the community of experts who have spent their whole lives researching and arguing about it, and have reached what certainly looks to me like a rough agreement.

You are welcome to hold anti-consensus views on global warming. In fact good science needs brave people like you to take the contrarian viewpoint. After all Galileo and Einstein also held anti-consensus positions at some point of time.

Your mistake would be to assume that merely holding a non-consensus view is itself success: historically these stalwarts of science eventually converted the contrarians to their side.

Ergo, we wait and watch, if history shows you were wrong then the world gets to laugh at you like we do now at the ancients who thought the world rides on the back of a turtle.

In addition to the very good climate-change resources that Scott commends (#13), please let me commend also Pascal Diethelm and Martin McKee’s well-referenced survey article “Denialism: what is it and how should scientists respond?“ Pascal and identify McKee identify five salient traits of denialist cognition as follows:

Scott: There is a difference when there is a consensus in math, physics, chemistry, and a consensus in climate science, or, say in social sciences. In the latter, the consensus is often based on flawed models which are not congruent to reality. When results are compared, often they are revised dramatically…this is often occurring in papers re climate science. The more complex and nonlinear the system, the more difficult the modelling becomes and the more susceptible to error and “black swan” events.
Crichton was not a scientist, but I am sure that Feynman would have totally agreed with him. I do not certainly mean that any autodidact crackpot can claim to challenge a consensus of scientific adepts. I do challenge the arrogance of so-called adepts to think their models brook no challenges. Published estimates of future warming, and future sea-levels often differ by an order of magnitude. If you go back to the early 70s and look at the Great Freeze consensus, you see the same.
Sure, usually I trust scientists in most fields. But many climate scientists are a different breed…they are operating in an ecosystem that is smarter than they are.
None of the above means that I am disagreeing with you about the warming except perhaps about the seriousness, which I think is speculation. And the whole field has become a political movement. I guess it boils down to how seriously you take climate science as a science. Meteorologists (another science) are mostly skeptical, as are engineers (Scott :)).
I take what is published about climate seriously, but I am, I think, rightly skeptical because of the limitations of extrapolation from limited models. And I think the precautionary principle would have everyone in caves.

At the risk of stating the obvious or repeating what someone might already have said, it should be noted that this episode reflects well on Lobos Motl. It’s quite remarkable how someone who hated you so back in 2006 was subsequently able to treat you like a human being. This invitation from him is a quite the olive branch.

Also, how do you continue to find so much time for distractions like blogging? I would have thought fatherhood would slow you down a bit. Myself, I find it hard enough just to find the time for my actual job, let alone all the wonderful distractions that don’t put food on the table.

Crichton was not a scientist, but I am sure that Feynman would have totally agreed with him.

LOL! I don’t think you get to dig Feynman from the grave and recruit his corpse into the climate-denialist movement, though a Google search reveals countless bloggers who’ve done exactly that (insisting that Feynman would have regarded AGW as “cargo cult science,” etc).

What do you make of the fact that the two theoretical physicists alive today who are arguably the most “Feynmannian”—Murray Gell-Mann and Steven Weinberg—are both on record strongly supporting the current scientific consensus on AGW, as is Stephen Hawking and pretty much every other celebrated physicist you’ve ever heard of, with Freeman Dyson the sole semi-skeptic that I know about? (Watch the Gell-Mann and Weinberg videos; they couldn’t possibly be more explicit.) Does that fact give you any pause? Let me guess: no?

Regarding the earth’s climate being a complex, nonlinear system that we don’t fully understand: I’ve always been blown away by the idea that the right response to that fact is to continue pumping billions of tons of CO2 into that complex nonlinear system every year, and see what happens! No, I don’t demand “proof” that a new technology is safe before anyone can use it: “proof” outside of pure mathematics is a concept for crackpots. But with such a massive uncontrolled experiment being carried out on the entire planet, and such a detailed prima facie case for the likely catastrophic effects of that experiment, it seems obvious to me that the burden should lie squarely with the deniers, to convince the scientific community that the current emissions levels pose merely an “acceptable” degree of risk. So far, they’ve noticeably failed to do so.

Also, how do you continue to find so much time for distractions like blogging? I would have thought fatherhood would slow you down a bit.

Well, it helps that my parents are here (and after they leave, Lily will be enrolling at MIT … the MIT daycare center, that is).

But also, you’re neglecting the possibility that I blog precisely as a way of avoiding all the other stuff I have to do! 🙂 (“Dana, I’d love to change her diaper, but you won’t believe what this commenter on Lubos’s blog named ‘TomVonk’ just wrote…”)

To me arguing about whether AGW exists or not is a little academic anyways: Even for someone who acknowledges AGW is there any realistic policy or conceivable technology that can do much to avert the damaging consequences much? What’s the model predicted response of climate to our best efforts.

Whatever greenhouse emissions we have reduced or are trying to reduce or even potentially can reduce in a best case scenario seems peanuts. Just hope that there may be some revolutionary technology or solution around the corner……

I will look at the Benestad link. Scott–do you really believe that climate science is evolved enough to make accurate, or even order of magnitude predictions? I am not a strong skeptic at all, and am mathematically and scientifically literate. I do object to the “NO DEBATE” marginalization of all skeptical questioning of models and wild-eyed pronouncements of doom. Just go to RealClimate sometime and, as a test, make a mildly critical comment 🙂 There are plenty of semi-skeptics. True believers tend to be dangerous people. It also seems to me that a “consensus on AGW” enfolds a hell of a lot of variability. I believe in a degree of AGW, but am a skeptic about the quality and reliability of many of the researchers involved and about the publicity machine attached to the acronym, along with the vituperation against any challenges to it.

do you really believe that climate science is evolved enough to make accurate, or even order of magnitude predictions?

Highly-accurate? No. Order-of-magnitude? Yes. I recommend reading the chapter on climate change in Nate Silver’s The Signal and the Noise. Silver makes a case that I found persuasive: namely, that if you simply used a crude, back-of-the-envelope physics calculation that took as input the amount of CO2 being emitted, and predicted on that basis how much extra heat the earth would trap—ignoring all nonlinearities, cloud effects, etc. etc.—you would have done a pretty good job at predicting the pattern of temperature increase that actually occurred over the past century. Furthermore, it’s not obvious that you would have done a better job by using the most sophisticated computer models of the climatologists. But the latter fact shouldn’t give too much comfort to the denialists, since the basic CO2/warming link remains as clear today as it was to John von Neumann in the 1950s.

If it doesn’t detract from my time reading your book, I may look at Silver’s one:) Looking at CO2 in isolation may not be enough to take in many other homeostatic mechanisms. Maybe it does. As I said earlier, I am no expert. The term “denialists” does not include me, btw. Even if the climate modelers are accurate, it would be useful for them to read the 1846 (and still in print) “Extraordinary Popular Delusions and the Madness of Crowds”.
Enough!!

We disagree on many things. I did order your book on Kindle, though, and look forward to reading it.

Nice dialogue on Lubos’ blog. From there I pulled a quote from Gordon:

“Climate science is highly unreliable because it is a swamp of parameters and chaotic systems and relies on big data. The people doing the research may be doing their best with the training they have, but ‘NO DEBATE’ is just a bullying, polemical statement.”

I have to agree. Some years ago when Stanford chemist Patrick Frank and I collaborated on a piece for Free Inquiry making this same point, I was dismayed to be tarred with the label “climate change denier,” as if I belonged in a conservative political camp. Neither Pat nor I are political conservatives — we just object to the methodology that substitutes models for theory. Neither do we deny that climate is changing, as it always has. Crazy world.

On a personal note, I was amused by your anecdote about summer camp and the “bunk trunk.” Years ago, my daughter looked forward to our shopping for “camp snacks” to give some relief from the notoriously bad camp cafeteria fare. In her second year, she had noted from the year before that many of the campers had foot lockers to store their treasures, and she insisted that she take the giant trunk I had inherited from my great grandfather — a battered old relic that barely fit in the back of the minivan — and could not be persuaded otherwise. What a sight it was, lugging that beast into the cabin. Being a fine arts camp, though, with a great number of individualists, even as young as they were — I was relieved that hardly an eyebrow was raised. And I never heard of them pooling anything, though I heard many stories of sharing everything. Would they have been so willing if they were compelled to do so? I doubt it.

A science-oriented climate-change site that consistently approaches the standards of Shetl Optimized in regard to wit, literacy, theory, and experimental observation is Neven’s Arctic Sea Ice Blog. Recommended.

T H Ray says “Neither do we deny that climate is changing, as it always has.”

Mark Schaal’s comment (#33) is correct that public discourse is best-served when skeptical assertions — in regard to climate chance or any other science-related topic … the feasibility of scalable quantum computation for example! — are stated as specifically as feasible.

Simple Solutions: Demagoguery depends upon the perception that political problems and solutions are easy to understand; while demagogues often grant that it may be difficult to implement their solution(s), they almost always assert that the basic concept of the solution is straightforward.

E.g. a stronger and more specific skeptical statement in regard to climate-change might be: “Elevated CO2 levels comparable to those of the present era have in the past been unaccompanied by ice-cap melting, sea-level rise, and elevated global temperatures.” Such strongly-skeptical statements have the considerable merit that the available scientific evidence (regarded as a body) directly addresses them.

Many of the acrimonious debates within science are really about very small differences of opinion, blown way out of proportion because a rare failure of Aumann’s Agreement Theorem makes everybody’s head explode. The split between Alchemistry and Chemistry was really one of Phlogiston vs. Oxygen. String theorists point out that they’ve made a lot of nontrivial progress on trying to explain quantum gravity, and that there are no competing ideas which have made nearly as much progress, while high energy physicists point out that nothing resembling the Standard Model is showing up in the theory yet. Computer scientists working on lower bounds point out that the ones working on upper bounds use simple primitive tools in very long tedious constructions to demonstrate small improvements, while ones working on upper bounds point out that the ones working on lower bounds use airy-fairy techniques to show that whole classes of things can’t work, without demonstrating any actual results.

In all the above cases where there was an argument about how to interpret the available evidence or how to make progress on an existing problem, there was (or is) a lot of seemingly contradictory indicators, and the acrimony is largely about how to interpret that data, not what the data actually says.

“Shwell Thanksh”: LOL! But I’m afraid O(1/ε2) messages are needed if you want agreement to within ε, with high probability over the shared prior. Maybe that’s our problem? (Actually, on reflection, no, it isn’t.)

That’s ridiculous. It does not follow that climate change (in the sense of mathematically general models that capture long term phenomena, such as self-organized criticality or punctuated equilibrium) is equivalent to computer-generated models of almost infinitely adjustable variables.

John Sidles # 34

My objections *are* specific.

I do want to make the point to both Mark and John, that I do personally think that the global warming trend is spiking. Whether that spike is from AGW or not, is simply irrelevant to the *science* of the matter, even if not to the sociology and politics.

It’s unclear to me which case you mean when you say technological interventions may help. If in the case of AGW, I think intervention will not help at all — in fact, will actually destabilize economies, governments and social structures to the detriment of us all. And in fact, I even foresee that this destabilization would happen on a larger scale and with more powerful positive feedback than that created even by all the little wars we’re engaged in, let alone the industrial activity generating greenhouse gases.

Applying the science of complex systems, however, and integrating information technology in a lateral fashion globally — in my opinion — has the effect of negative feedback. That is, a self-organized distribution of information and resources would be preferred to the hierarchical top-down enforcement of a common standard of atmospheric carbon reduction. It’s also good insurance against the global warming spike, whether the spike is temporary or permanent, because it networks resources to need on a timely basis; i.e., just as temperatures do not spike uniformly, societies need not respond uniformly. What we do need to do for the common good, is recognize the common threat and prepare against it with a rapid-response network whose hubs and nodes have the capacity to change direction quickly. Blanket political agreements don’t do that, often create conflict, and are unreliably enforced as well.

The denialists forget that the basics of climate change have nothing to do with computer models and everything to do with basic physics and arithmetic. Models are for working out the details, but the bigger picture emerges from pretty simple principles.

Scott #38: I’m missing something really basic trying to understand that paper. It appears to be saying that the basic protocol is that the two parties just repeat back and forth what they think the probability is until they’re in agreement, but don’t they need to compare notes on what they actually think? For example, let’s say that the agreed upon prior is that a person has three children, two girls and a boy, and the question is whether the oldest is a girl. The two counterparties each know that a specific girl isn’t the oldest, making them each think of the probability as being 1/2, but to come to full agreement they need to compare notes to see if they’re talking about the same girl, which determines whether the probability should be 1/2 or zero. How is that supposed to be handled?

Bram: Interesting example, but you need to precise about the question! If the question is:

“Is the oldest child a girl?”

then the two parties agree before they even start: namely, they both agree that

Pr[oldest child is a girl] = 1/2.

(What we mean by agreement, in this setting, is just that they assign the same or nearly the same probabilities to the event in question.)

If you asked a different question, then the parties’ different knowledge might lead them to assign different probabilities. But then, if you try out an example, you’ll find that the parties do necessarily learn new things just by telling each other their probabilities. That’s basically the content of Aumann’s Theorem, which I encourage you to look at the original proof of (forgetting my complexity-theoretic version for the time being!). There are few results with a larger ratio of

Shwell #37, Scott #38 : Obviously Bayesian updating will not converge if the considered hypotheses include conspiracy theories (involving left-wing academics one side and greedy oil companies on the other).

Even without that, Bayesian updating will be *very* slow if every piece of evidence invokes its own Bayesian process to determine if the origin of this evidence is credible, if the authors were biased etc.

In other words Bayesian inference will not work well in a quasi-infinite dimensional problem space, which includes almost everything, from weather stations and tree rings to stolen emails and Al Gore’s business deals etc. …

Scott, I understand Aumann a little bit better now, and on top of it requiring that we both be completely honest rational agents, both have full faith that the other person is a perfectly honest rational agent, both have full faith that the other has full faith etc. etc. It doesn’t even imply what I thought!

What I really want to know is, what is the communication complexity of us coming within epsilon of finding out what an agent who knew our combined sets of information would think? Is it still only dependent on epsilon or is it dependent on the size of our knowledge bases?

Bram #46: Yes, you’re right, to understand Aumann’s Theorem is also to understand many possible reasons for its limited relevance in the real world! 🙂

Your question is a good one, and the answer is that O(1/ε2) bits still suffice for that task, independent of the size of the knowledge bases. I even show that somewhere in my paper, as a lemma along the way to proving a convergence between Alice and Bob.

Scott #47, I might be missing something, but everything in your paper seems to be about Alice and Bob coming to *agreement*, and a bunch of the optimizations to coming to agreement seem to be about coming to agreement sooner by sending less data so you don’t realize that your data gets more confusing when all put together, hence the concept of noise being a good thing. To truly figure out what an agent who knew their total combined knowledge would think, the peers have to go beyond simply saying their probabilities, because of simple cases like we two digits written down and I say the chances of them being 99 are 1/10 because I know the first digit is 9 and you say it’s 1/10 because you know the second digit is 9, and anything vaguely resembling the standard protocol will result in us agreeing that it’s 1/10, even though we really should come to a combined probability of 1.

Another way in which your paper deviates from reality – When Alice communicates a value to Bob, in the real world it might be very computationally expensive for Bob to figure out how Alice could possibly have come to that state, and that isn’t factored in as something which can happen. As a general rule, this is what has happened whenever anybody responds to a non-misheard statement with ‘What?’

Bram #48: Regarding the computational cost of Alice and Bob updating their priors—the entire second part of my paper (the technically much more involved part) is all about that question! You might disagree with how I formalized “computational cost,” but at least take a look before commenting about how the paper deviates from reality, fails to factor in something so obvious, etc. 😉

Regarding your first point: yes, it’s true that if Bob wants to know all the evidence on which Alice based her opinion, then Alice needs to communicate all that evidence to Bob, and vice versa! I don’t see any conceivable way around that. The surprising part—the part that goes against some people’s intuitions—is that if Alice and Bob just want to agree on an answer (and not on the underlying evidence), then vastly less communication suffices. I hope I was clear enough in the paper about the distinction.

Yes, you do talk about calculating priors and mention that there are other factors which could cause computational cost, I was just pulling out one particular one of those.

I’m not totally sure it’s impossible to do better than peers communicating what they know. The first step would be trying to find a point of disagreement even after the shared probability has been agreed upon, maybe by discussing hypothetical scenarios?